A small wedge whose base is horizontal is fixed to a vertical rod as shown in fig . The sloping side of the weidgeis frictionless and the wedge is span with a constant angular speed `omega` about vertical axis as shown in the fig find the
a. value of angular speed `omega ` for which the block of mass `m` just does not slide down the wedge.
b. normal reaction on the block by wedge when block does not slip relative to wedge.

Explanation

The free body diagram of the block is
a. For block not to slide wedge appling Newton's second law along incline we get
`mg sin theta = m omega^(2)(l cos theta) cos theta`
` omega = sqrt((g sin theta)/(1 cos theta))`
b. Appling Newton 's second law along normal to the wedge

we get `N = mg cos theta + m omega^(2)(1 cos theta) sin theta`
`= mg cos theta + m(g sin theta)/(1 cos^(2) theta) 1 cos theta sin theta = mg sec theta`